Random matrix theory has become increasingly important in wireless communication theory. Since comprehensive literature on this topic is not available, both students and senior researchers new in this field have a hard time to enter this promising field. This summer school breaks down random matrix theory for wireless communications into 6 short courses taught by experts in the engineering community. The curricula of this 6 short courses are interconnected and can only be taken as a combined package due to interdependencies between the presented material. The summer school is intended for students with a background in communications engineering and is given in form of 23 hours of lectures.
Random Matrix and Free Probability Theory – Prof. Ralf R. Müller – 5 hours: 0.65 ECTS
Semicircle law, quarter circle law, Stieltjes transform, Marcenko-Pastur distribution, Stieltjes inversion formula, non-commutative random variables, asymptotic freeness, additive and multiplicative free convolution, R-transform, S-transform, free central limit theorem
Introduction to Convergence of Probability Measures – Dr. Jamal Najim – 3 hours: 0.4 ECTS
Convergence of probability measures. Convergence in distribution, in probability and almost sure. Convergence of empirical probability measures. Useful tools to prove the convergence of probability measures: Borel-Cantelli’s lemma, the Laplace transform of probability measures.
Stieltjes Transform Method – Prof. Philippe Loubaton and Asoc. Prof. Walid Hachem – 4 hours: 0.5 ECTS
Properties of the Stieltjes transform, connections with the convergence of probability measures, convergence of the Stieltjes transform of the empirical eigenvalue distributions of certain random Gram matrices.
Estimation Using Random Matrices in Multi-antenna Settings – Dr. Xavier Mestre – 3 hours: 0.4 ECTS
Application of random matrix theory to the design of array signal processing algorithms for low sample support. Derivation of the most important G-estimators for covariance-type matrices. Some applications in communications and signal processing.
Statistical Mechanics of Wireless Communications – Ass. Prof. Aris Moustakas – 5 hours: 0.65 ECTS
Diagrammatic approach to random matrix theory and applications to communications. Statistical physics framework, replicas and its applications to multi-antenna systems and CDMA.
Applications of random matrix theory to vector channels – Dr. Laura Cottatellucci – 3 hours: 0.4 ECTS
Practical approaches to the determination of metrics of interest in telecommunications: relationship between channel capacity and SINR to probability density functions, Stieltjes transforms, eigenvalue moments. Comparative study of different methods by the different insights they provide on communication systems.